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# Structural constraints for the off-axis three-mirror system

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Hi everyone, I have a question for you.

I want to design an off-axis three-mirror imaging system (in sequential mode) but I don't understand how to control the five distances pictured in the image below.

I'm looking for a way to avoid light obscuration and prevent surface interference when optimizing.

Until now, I tried to control the distances using the global vertex coordinates MFE operands without success. Any suggestion would be really appreciated.

Thank you.

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Best answer by MichaelH 19 September 2023, 22:41

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Userlevel 5
+3

I'm guessing the system is in the YZ plane.  Insert perpendicular dummy planes at your arrows.  Set airspaces as variables and use differences in RAGY, RAGZ values at the dummy planes and mirror surfaces to bound Y and Z.

Userlevel 6
+2

Hey Lorenzo,

If you consider the outer marginal rays as vectors and realize that the shortest distance between the marginal ray (vector a) and the edge of the mirror (point m) will be a point that makes a perpendicular vector (vector b).  Once you calculate b, you can then make sure this has a minimum value so the mirror doesn’t clip the beam:

You can create a ZPLM optimization operand which performs this calculation for you.  One problem with the ZPLM is that you have limited inputs (when I first wrote this ZPLM, you only had 4 inputs but now you have 6 inputs).

The attached ZIP file has a PDF showing how to use the ZPL33.zpl example macro which performs this calculation.